What is the largest slick that will fit an s 10 without sectioning the rear frame. Will be tubed.

The first thing the tire will hit is the leaf spring. The offset of the wheel will have the biggest effect. I believe you can get a 10.5" on a 10" wheel if you have about 4.5" backspace.
http://www.v8s10.org/forum/

I'm 99% sure my dads S10 has not had the frame moved in, we run a 29.5-10.5W on a 12" rim with 3" BS (Weld Alumastar)and its really close to the leaf spring ,also have a set of 11" Hosehots with 2-7/8" BS and they have plenty of room. Backspacing is the key.